This section is intended to introduce the reader to various aspects of art, which may be related to various aspects of the present principles that are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present principles. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.
Digital watermarking consists in modifying a multimedia content in a robust and imperceptible way, in order to hide a secret message. Applications of watermarking range from broadcast monitoring to copyright protection through meta-data binding. In particular, robust watermarking methods are essential components of content protection architectures. The embedded message (referred to as the watermark payload) indeed constitutes a forensic piece of evidence for traitor tracing tasks, e.g. by identifying a leak when a content is illegally made available on the Internet.
The popularity of 3D generated models has created the need for dedicated methods designed to tackle robust watermarking of meshes. Meshes are assumed to be piecewise-linear approximations of the surface boundary of 3D objects. They are formally defined by a set V of nv vertices, a set E of ne edges and a set F of nf facets. 3D watermarking methods focus on the common triangle mesh representation. 3D watermarking for animated meshes is a technical domain with focus on watermarking of meshes which have already been animated. In this context, the mesh is not only characterized by its set of vertices V, edges E and faces E, but also by the position of the vertices throughout the animation (the time component).
For animated meshes, Agarwal et al. disclose in “Robust blind watermarking mechanism for motion data streams” (Proceedings of the 8th workshop on Multimedia and security, pp. 230-235, 2006) a watermarking algorithm based on the dynamics of the mesh skeleton. The skeleton corresponds to a set of joints and bones virtually attached to the vertices of the input model. By modifying the relative positioning of the different bones composing the skeleton, the vertices are moved accordingly in some kind of elastic fashion, thereby granting the animation creator with the ability to pose the 3D model in any desired way. A pose is an isometric transformation of the 3D mesh, i.e. all geodesic distances between pairs of surface points are preserved. For a humanoid 3D object, a pose corresponds for instance to raising an arm, extending a leg, etc. As a result, by defining a temporal sequence of poses, it is possible to design an animation e.g. the walking cycle of a character. This animation can be done manually by an artist or by using motion capture (MOCAP) devices to record the movements of a performing actor. The method disclosed by Agarwal et al. embeds the watermark by altering the temporal trajectory of some elements of the 3D model, such as joints or vertices. In their preferred embodiment, such an embedding is based on a wavelet decomposition of the space-curve associated with the temporal trajectory. In other words, the animation of the mesh is modified but not the mesh itself. As such, a limitation of this technique is that (i) changing the animation of the 3D object discards the watermark and (ii) the watermark cannot be recovered from a single pose of the animation. A method for 3D meshes that embeds a watermark in the geometry of the mesh in a way that is pose-invariant, and thus oblivious to animation parameters, is therefore desirable.
In prior work, the challenge of pose invariance in 3D mesh watermarking has been tackled using geodesic distances. The geodesic distance refers to the shortest path on the surface of the object between two points of a 3D object. As mentioned earlier, such distances are expected to be barely affected by poses taken by the object during the temporal animation. In “Surface-Preserving Robust Watermarking of 3D Shapes” (IEEE Transactions on Image, Processing, vol. 20, pp. 2813-2826, 2011), A. G. Bors and M. Luo disclose a watermarking method relying on watermarking the histogram of the geodesic distances between the vertices and a pseudo-random reference point on the surface of the object. While this watermarking technique is oblivious to animation, it also has two major limitations, one being inherent to the use of geodesic distances. First, geodesic distances are highly sensitive to noise addition and thus provide limited watermark robustness against this type of attack. Second, the use of a pseudo-random reference point makes the watermarking system very weak against desynchronization attacks such as cropping. A method for 3D meshes that embeds a watermark in the geometry of the mesh in a way that is pose-invariant and robust to a large range of attacks is therefore needed.